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Math Help - equation-geometrical

  1. #1
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    equation-geometrical

    1. Find the value for c for which y=x+c is a tangent to y=3-x-5x^2

    don't understand what to do
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  2. #2
    Math Engineering Student
    Krizalid's Avatar
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    You gotta find first the intersection of the line and the curve, so

    x+c=3-x-5x^2\implies5x^2+2x+(c-3)=0.

    Now, so that the line be tangent to the curve, the discriminant of the previous equation must be zero, so 4-4\cdot5(c-3)=0\implies1-5(c-3)=0.

    Solvin' for c yields the desired answer.
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  3. #3
    MHF Contributor red_dog's Avatar
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    The system formed by the two equations must have an unique solution.
    Plug y from the first equation in the second and you'll obtain a quadratic equation. Put the condition that \triangle =0, where \triangle =b^2-4ac (a,b,c are the coefficients of the quadratic equation).
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